Heegner Modules and Elliptic Curves
Edition: 1 edition
Publisher: Springer
Published: August 26, 2004
Language: eng
Format: Paperback
Number of pages: 517
ISBN-13: 9783540222903
Subjects: Algebraic geometry; Science/Mathematics; Homology theory; Mathematics; Geometry - Algebraic; 11F52, 11G05, 11G09, 11G15, 11G40, 11R58,; 14F20, 14G10, 14H52, 14J27, 14K22; Drinfeld Modules; Elliptic Curves; Heegner Points; Mathematics / Number Theory; Tate Conjecture; Tate-Shafarevich Groups; Number Theory; Algebraic fields; Curves, Elliptic
First sentence: The points of departure of this text are twofold: first the proof by Drinfeld in 1974 ([Drl], see also Appendix B) of an important case of the Langlands conjecture for GL2 over a global field of positive characteristic and second the proof by Kolyvagin [K] in 1989 of the Birch Swinnerton-Dyer conjecture for a class of Weil elliptic curves over the rational field Q.
Description: Heegner points on both modular curves and elliptic curves over global fields of any characteristic form the topic of this research monograph. The Heegner module of an elliptic curve is an original concept introduced in this text. The computation of the cohomology of the Heegner module is the main technical result and is applied to prove the Tate conjecture for a class of elliptic surfaces over finite fields; this conjecture is equivalent to the Birch and Swinnerton-Dyer conjecture for the corresponding elliptic curves over global fields.
Notes: Lecture Notes in Mathematics